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   <title>Building the Bounds Matrix</title>
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<a name="Building_the_Bounds_Matrix"></a>Building the Bounds Matrix</h2>
The distance bounds matrix for each molecule contains lower bounds for
each atom--atom distance in the lower triangle and the upper bounds for
each distance in the upper triangle. These bounds are assigned using a
rules-based approach [<a href="References.htm#Blaney1994">Blaney1994</a>]
where 1--2, 1--3, and some 1--4 distances are set using the force
field's bond length, bond angle, and torsion parameters respectively.
Bounds for some higher order distances (typically associated with
rings) are also set. Any remaining distance bounds are set to
conservative defaults: with a minimum above the sum of van der Waals
radii and a large maximum.<br>
<br>
Once the bounds matrix is constructed, it is refined using a triangle
bounds smoothing algorithm that iteratively shrinks the individual
bounds until they are as tight as possible.[<a
 href="References.htm#Crippen1981">Crippen1981</a>]<br>

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